A pool has a uniform cross-section of radius 5 m and uniform depth 1.4 m. It is filled by a pipe whichdelivers water at the rate of 25 litre per second. Calculate in minutes, the time taken to fill the pool. If thepool is emptied in 29 minutes 10 seconds by another cylindrical pipe through which water flows at m per second, calculate the radius of the pipe in cm.
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Volume of pool =πR
2
h=π×5×5×1.4=35πm
3
=3500π litres
Volume of water coming out =50L per second
Time taken to fill the tank =
50
35000π
sec
=
50×7×60
35000×22
min
=36.67 min
Let radius of pipe be
′
r
′
cm. Then
Volume of water coming out from pipe in 1 sec, =(πr
2
×200)cm
3
Time required to empty =42min=42×60 sec
⇒
πr
2
×200
35×10
6
cm
3
×π
=42×60
⇒r
2
=
42×60×200
35×10
6
=69.44cm
⇒r=
69.44
=8.33cm
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